Problem: What is the surface area of a cylinder with base radius $4$ and height $6$ ? $4$ $6$
Solution: The areas of the top and the base are simply the area of a circle: $\pi r^2 = \pi \cdot 4^2 = 16 \pi$ The lateral surface area is the same as the area of a rectangle with height $6$ and width equal to the circumference of the base. That circumference is $2 \pi r = 2\pi \cdot 4 = 8\pi$ Thus, the lateral surface area is $wh = 8 \pi \cdot 6 = 48 \pi$ The total surface area is $16 \pi + 16 \pi + 48 \pi = 80\pi$.